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Concept# Champernowne constant

Summary

In mathematics, the Champernowne constant C10 is a transcendental real constant whose decimal expansion has important properties. It is named after economist and mathematician D. G. Champernowne, who published it as an undergraduate in 1933.
For base 10, the number is defined by concatenating representations of successive integers:
:C10 = 0.12345678910111213141516… .
Champernowne constants can also be constructed in other bases, similarly, for example:
:C2 = 0.11011100101110111… 2
:C3 = 0.12101112202122… 3.
The Champernowne word or Barbier word is the sequence of digits of C10 obtained by writing it in base 10 and juxtaposing the digits:
: 12345678910111213141516...
More generally, a Champernowne sequence (sometimes also called a Champernowne word) is any sequence of digits obtained by concatenating all finite digit-strings (in any given base) in some recursive order.
For instance, the binary Champernowne sequence in shortlex order is
: 0 1 00 01 10 11 000 001 ...
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